If the equation a n xⁿ + a n - 1 xⁿ⁻¹ +........... + a₁x = 0 a₁ ≠ 0,n ≥ 2, has a positive root x = α, then the equation n a n xⁿ⁻¹ + (n - 1)a n - 1 xⁿ⁻² +........... + a₁ = 0 has a positive root, which is

(C) greater than or equal to smaller than α

Limit, Continuity and Differentiability: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q2693

JEE Main 2005Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

If the equation

{a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0

{a_1} \ne 0,n \ge 2,

has a positive root

x = \alpha

, then the equation

n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ........... + {a_1} = 0

has a positive root, which is